The ratio of the K.E. required to the given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

Options

A. `1`
B. `2`
C. `1//2`
D. `oo`

Answer

B

Explanation

K.E. required for satellite to escape from the earth's gravitational field `1/2mv_(e)^(2)=1/2m(sqrt((2GM)/R))^(2)=(GMm)/R`
K.E. required for satellite to move in circular orbit
`1/2mv_(0)^(2)=1/2m(sqrt((2GM)/R))^(2)=(GMm)/(2R)`
The ratio between these two energies `=2`